Heretofore, as a dendrimer-like star polymer, a compound and a method for producing the same described below are known (refer to Non-Patent Document 1).
In a first step, a star polymer having a specific molecular weight, which includes three PEO arms, is synthesized by a core-first method using 2-ethyl-2-hydroxymethyl-1,3-propanediol. All three hydroxy groups (a) efficiently initiate polymerization of ethylene oxide to produce a product having Poisson molecular weight distribution. In the same manner, a PEO star polymer including four arms can be prepared using pentaerythritol (e).
In a second step, a terminal OH group is chemically modified with an acid halide to prepare star type macroinitiators (c) and (g).
In a final step, an amphiphilic star copolymer is synthesized by the growth of a polystyrene block in the presence of copper bromide/BiPy with respect to the star type macroinitiators (c) and (g) (refer to Scheme 2 of Non-Patent Document 1).
As the same dendrimer-like star polymer, the other compound as shown in the formula shown below, and a method for producing the same are known (refer to Non-Patent Document 2)

First, in the presence of dipiperidinoethane, an oligomer of butadiene is fabricated and then subjected to block addition polymerization with styrene to prepare a block copolymer including a polystyrene block and short 1,2-polybutadiene. A double bond of a side chain of a 1,2-polybutadiene unit is hydrosililated and then a living chain of 1,4-polybutadiene lithium or P2VPK is added to produce a star polymer of an umbrella structure (refer to Scheme 98 of Non-Patent Document 2).    [Non-Patent Document 1]
Macromolecules 2000, 33, 5418-5426 (2000)    [Non-Patent Document 2]
Chem. Rev. 2001, 101, 3747-3792 (2001)